Are two permutations conjugate?
Returns TRUE if two permutations are conjugate and FALSE
otherwise.
are_conjugate(x, y) are_conjugate_single(a,b)
x,y,a,b |
Objects of class permutation, coerced to cycle form |
Two permutations are conjugate if and only if they have the same shape.
Function are_conjugate() is vectorized and user-friendly;
function are_conjugate_single() is lower-level and operates
only on length-one permutations.
The reason that are_conjugate_single() is a separate function
and not bundled inside are_conjugate() is that dealing with the
identity permutation is a pain in the arse.
Returns a vector of Booleans
The functionality detects conjugateness by comparing the shapes of two
permutations; permutations are coerced to cycle form because function
shape() does.
Robin K. S. Hankin
are_conjugate(rperm(20,3),rperm(20,3)) rperm(20,3) %~% cycle(1:3) z <- rperm(300,4) stopifnot(all(are_conjugate(z,id)==is.id(z))) data(megaminx) stopifnot(all(are_conjugate(megaminx,megaminx^as.cycle(sample(129)))))
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